jP_{initial}jP_{final}MOMENTUM PRINCIPLESForce and MotionCP-03Page 8Rev. 0Figure 1 MomentumThe development of the law of conservation of momentum does not consider whether thecollision is elastic or inelastic. In an elastic collision, both momentum and kinetic energy (i.e.,energy due to an objects velocity) are conserved. A common example of an elastic collision isthe head-on collision of two billiard balls of equal mass. In an inelastic collision, momentum isconserved, but system kinetic energy is not conserved. An example of an inelastic collission isthe head-on collision of two automobiles where part of the initial kinetic energy is lost as themetal crumples during the impact. The concept of kinetic energy will be discussed further inModule 5 of this course.The law of conservation of momentum can be mathematically expressed in several differentways. In general, it can be stated that the sum of a system's initial momentum is equal to the sumof a system's final momentum.(3-7)In the case where a collision of two objects occurs, the conservation of momentum can be statedas follows.P+ P= P+ P(3-8)1 initial2 initial1 final2 finalor(m v )+ (m v )= (m v )+ (m v )(3-9)1 1 initial2 2 initial1 1 final2 2 finalIn the case where two bodies collide and have identical final velocities, equation 3-10 applies.m v + m v = (m + m )v(3-10)112212fFor example, consider two railroad cars rolling on a level, frictionless track (see Figure 1). Thecars collide, become coupled, and roll together at a final velocity (v ). The momentum beforefand after the collision is expressed with Equation 3-10.